Yes, today's Gospel is the famous "wineskins" passage from Mark. Jesus' disciples (and implicitly Jesus himself) have been weighed on the scales of devotion and found wanting because, unlike the disciples of John the Baptist and the Pharisees, Jesus' followers are not exactly noteworthy for their ascetical practices. They don't even fast!
In the first reading, from the First Book of Samuel in the Old Testament, King Saul is berated (and ultimately condemned to lose the crown) for the opposite problem: he was so zealous to offer impressive sacrifices to the Lord that he let his men take the best animals from the vanquished Amalekites and offer them up--instead of destroying them under the "ban of destruction" as commanded. (I suppose Saul couldn't stand the thought of wasting those perfectly good animals.)
While the whole concept of a "ban of destruction" (basically a "scorched earth policy") is abhorrent to us today (though it is still practiced), it could be that God's command was an attempt to bring Saul and the people a step closer to "worship in spirit and truth" that would not involve destruction and animal sacrifices. But that was like sewing fresh cloth on an old garment: Saul overruled God's explicit command in order to bring God what God did not want in the first place (and what Psalm 40 would later say that God "did not delight in" anyway).
The old approach to sacrifice that Saul clung to (and that Jesus' questioners also presume) is that it is the object offered (whether in sacrifice or in self-discipline) that wins God favor. The new wine is that obedience to God's command (a form of God's self-expression) is the surrender, gift, offering, sacrifice of the person in their interiority given to God himself.
Remember the Morning Offering? It encapsulates that gift of self, and puts it (right where it belongs!) in the context of the complete gift that Jesus makes to the Father (and to us) in the Mass!